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Flash supports two types of image formats: vector and bitmap. Vector graphic files consist of an equation that describes the placement of points and the qualities of the lines between those points. Using this basic logic, vector graphics tell the computer how to display the lines and shapes, as well as what colors to use, how wide to make the lines, where to put it on the Stage, and at what scale. Flash is a vector program. Thus, anything that you create with the Flash drawing tools will be described in vector format. Vector graphics have some important benefits: They re small in file size and they scale accurately without distortion. However, they also have a couple of drawbacks: Highly complex vector graphics may result in very large file sizes, and vectors aren t really suitable for creating continuous tones, photographs, or artistic brushwork.



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You can strongly brand an application s appearance with fonts that are unique to a particular company s design standards. Embedded fonts support anti-aliasing, which enables you to control the sharpness of the font to a fine degree.

Now suppose that the sequence s = [sl, s2, . . . ,s,] is transmitted over a BSC and that the received sequence is R = [q, . . . , r,]. Because of independent noise samples, the r2, likelihood function factors,

pj i, j ,





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The maximum a posteriori (MAP) decoding algorithm suitable for estimatingbit and/or state probabilitiesfor a finite-stateMarkov system is frequently referred to as the BCJR algorithm, after Bahl, Cock, Jelenik, and Raviv who proposedit originallyin [111 The BCJR algorithm computes the posterior probability of symbols from Markov sources transmitted through discrete memoryless channels Since the output of a convolutional coder passed through a memoryless channel (such as an AWGN channel or a BSC) forms a Markov source, the BCJR algorithm can be used for maximum aposteriori probabilitydecoding of convolutional codes In many respects, the BCJR algorithm is similar to the Viterbi algorithm However, the Viterbi algorithm computes hard decisions -even if it is employing soft branch metrics -since a single path is selected to each state at each time.

For our purposes, the 2n term drops out of the equations, and this needlessly complicates them. This formulation is similar to the Ewald spheres approach used in crystallography. As a sanity check, we can confirm that if the reference and object beams are opposite from each other in an inline configuration, the difference between them is the sum of their magnitudes:

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This result in an overall decision on an entire sequence of bits (or codeword) at the end of the algorithm, and there is no way of determining the reliability of the decoder decisions on the individual bits Furthermore, the branch metric is based upon log likelihood values; no prior information is incorporated into the decoding process The BCJR algorithm, on the other hand, computes soft outputs in the form of posterior probabilities for each of the message bits While the Viterbi algorithm produces the maximum likelihood message sequence (or codeword), given the observed data, the BCJR algorithm produces the a posteriori most likely sequence of message bits, given the observeddata (Interestingly, the sequenceof bits produced by the MAP algorithm may not actually correspond to a continuous path through the trellis.

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) In terms of actual performance on convolutionalcodes, the distinction between the Viterbi algorithm and the BCJR algorithm is frequently insignificant,since the performance of the BCJR algorithm is usually comparable to that of the Viterbi algorithmand any incrementalimprovementoffered by the BCJR algorithm is offset by its higher computational complexity However, there are instances where the probabilities produced by the BCJR are important For example, the probabilities can be used to estimate the reliability of a decisions about the bits This capability is exploited in the decoding algorithms of turbo codes As a result, the BCJR algorithm lies at the heart of most turbo decoding algorithms We first express the decoding algorithmin terms of probabilitiesthen,in Section 14312, we present analogous results for likelihood ratio decoding The probabilistic description is more general, being applicable to the case of nonbinary alphabets However, it also requires particular care with normalization.

// Create the thread. thid = sceKernelCreateThread( update_thread , CallbackThread, 0x11, 0xFA0, 0, 0); if (thid >= 0) { sceKernelStartThread(thid, 0, 0); } } /* Main Function */ int main() { pspDebugScreenInit(); SetupCallbacks(); printf( Hello World! ); sceKernelSleepThread(); // Return success. return 0; }

Furthermore, there are approximationsthat can be made in association with the likelihoodratio formulationthat can reduce the computationalburden somewhat..

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